Cook lasagna pasta according to box directions. Drain then lay flat on a sheet of aluminum foil.
Heat oven to 350 F. Lightly oil a 13-inch by 9-inch baking dish or spray with non-stick cooking spray.
Heat the olive oil in a wide skillet with sides over medium heat. Add onion and cook, stirring occasionally until translucent, about 5 minutes. Add the garlic, red pepper flakes, zucchini, squash, stirring occasionally until softened but still with some crunch, another 5 to 8 minutes.
Stir in the roasted red peppers and crushed tomatoes. Bring to a low simmer and cook until the liquid has thickened and reduced by half, about 5 minutes. Add the basil.
Spoon just enough vegetable mixture into the baking dish to lightly cover the bottom (about 1 cup). Arrange four noodles lengthwise and side by side to cover the bottom. Spread about half of the ricotta cheese mixture over the noodles. Sprinkle with a third of the parmesan cheese and a third of the mozzarella cheese. Top with a third of the vegetable mixture.
Add another layer of four noodles then repeat with remaining cheese and vegetables. Finish with a final layer of noodles, vegetables, parmesan cheese and mozzarella cheese.
Cover loosely with aluminum foil and bake 20 minutes, uncover then bake 15 minutes until cheese is crusty around the edges. To make the cheese golden brown on top, slide under the broiler for 1 to 2 minutes. Let rest 10 to 15 minutes before serving.